0.10 The ideal gas law  (Page 7/7)

Sketch a graph with two curves showing Pressure vs. Volume for two different values of the number of molesof gas, with $n_2> n_1$ , both at the same temperature. Explain the comparison of the twocurves.

Sketch a graph with two curves showing Pressure vs. 1/Volume for two different values of the number ofmoles of gas, with $n_2> n_1$ , both at the same temperature. Explain the comparison of the twocurves.

Sketch a graph with two curves showing Volume vs. Temperature for two different values of the number ofmoles of gas, with $n_2> n_1$ , both at the same pressure. Explain the comparison of the twocurves.

Sketch a graph with two curves showing Volume vs Temperature for two different values of the pressure ofthe gas, with $P_2> P_1$ , both for the same number of moles. Explain the comparison of thetwo curves.

Explain the significance of the fact that, in the volume-temperature experiments, $\frac{\beta }{\alpha }$ is observed to have the same value, independent of the quantity of gas studied and the type of gas studied. What is the significanceof the quantity $\frac{\beta }{\alpha }$ ? Why is it more significant than either $\beta$ or $\alpha$ ?

Amonton's Law says that the pressure of a gas is proportional to the absolute temperature for a fixed quantity of gas in a fixedvolume. Thus, $P=k(N, V)T$ . Demonstrate that Amonton's Law can be derived by combining Boyle's Law and Charles'Law.

Using Boyle's Law in your reasoning, demonstrate that the "constant" in Charles' Law, i.e. $k_2(N, P)$ , is inversely proportional to $P$ .

Explain how Boyle's Law and Charles' Law may be combined to the general result that, for constant quantity of gas, $\times (P, V)=kT$ .

Using Dalton's Law and the Ideal Gas Law, show that the partial pressure of a component of a gas mixturecan be calculated from

Where $P$ is the total pressure of the gas mixture and $X_i$ is the mole fraction of component $i$ , defined by

Dry air is 78.084% nitrogen, 20.946% oxygen, 0.934% argon, and 0.033% carbon dioxide. Determine the molefractions and partial pressures of the components of dry air at standard pressure.

Assess the accuracy of the following statement:

Boyle's Law states that $PV=k_1$ , where $k_1$ is a constant. Charles' Law states that $V=k_{2}T$ , where $k_2$ is a constant. Inserting $V$ from Charles' Law into Boyle's Law results in $P{k}_{2}T=k_1$ . We can rearrange this to read $PT=\frac{k_1}{k_2}=\text{a constant}$ . Therefore, the pressure of a gas is inversely proportional to the temperature of the gas.

In your assessment, you must determine what information is correct or incorrect, provide the correctinformation where needed, explain whether the reasoning is logical or not, and provide logical reasoning where needed.